Abstract
An explicit classification of homogeneous quaternionic Kahler structures by real tensors is derived and we relate this to the representation-theoretic description found by Fino. We then show how the quaternionic hyperbolic space \({\mathbb H}H(n)\) is characterised by admitting homogeneous structures of a particularly simple type. In the process we study the properties of different homogeneous models for \({\mathbb H}H(n).\)
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Lopez, M., Gadea, P. & Swann, A. Homogeneous Quaternionic Kahler Structures and Quaternionic Hyperbolic Space. Transformation Groups 11, 575–608 (2006). https://doi.org/10.1007/s00031-005-1124-3
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DOI: https://doi.org/10.1007/s00031-005-1124-3